Solve: Adding 1/2 and 2/8 - Fraction Addition Practice

Fraction Addition with Common Denominators

Solve the following exercise:

12+28=? \frac{1}{2}+\frac{2}{8}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem step by step.
00:08 First, we'll multiply the fraction by 4 to get a common denominator.
00:13 Remember, when we multiply a fraction, we need to multiply both the top number (numerator) and bottom number (denominator).
00:21 Now, let's work out these multiplications carefully.
00:26 Next, we can add the fractions since they now have the same denominator.
00:31 Let's add the numbers in the numerator while keeping the same denominator.
00:36 And there we have it! That's our final answer to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

12+28=? \frac{1}{2}+\frac{2}{8}=\text{?}

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Identify the given fractions 12\frac{1}{2} and 28\frac{2}{8}.
  • Step 2: Determine a common denominator for both fractions. Since 8 is a multiple of 2, we will use 8 as the common denominator.
  • Step 3: Convert 12\frac{1}{2} to an equivalent fraction with a denominator of 8.
  • Step 4: Add the fractions together.

Now, let's work through these steps:

Step 1: The fractions given are 12\frac{1}{2} and 28\frac{2}{8}.

Step 2: We choose 8 as the common denominator because it is a multiple of 2.

Step 3: Convert 12\frac{1}{2} to have a denominator of 8. To do this, multiply both the numerator and the denominator of 12\frac{1}{2} by 4:

12=1×42×4=48 \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}

The fractions now are 48\frac{4}{8} and 28\frac{2}{8}, both having the common denominator 8.

Step 4: Add the numerators of these fractions:

48+28=4+28=68 \frac{4}{8} + \frac{2}{8} = \frac{4+2}{8} = \frac{6}{8}

Therefore, the sum of 12+28\frac{1}{2} + \frac{2}{8} is 68 \frac{6}{8} .

3

Final Answer

68 \frac{6}{8}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominator before adding numerators together
  • Technique: Convert 12 \frac{1}{2} to 48 \frac{4}{8} by multiplying by 4
  • Check: Verify 48+28=68 \frac{4}{8} + \frac{2}{8} = \frac{6}{8} by adding numerators ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 12+28 \frac{1}{2} + \frac{2}{8} as 310 \frac{3}{10} = wrong answer! This ignores that fractions represent parts of different wholes. Always convert to common denominators first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \)\( \frac{4}{5}+\frac{1}{5}= \)

FAQ

Everything you need to know about this question

Why can't I just add 1+2 and 2+8 to get 3/10?

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Because fractions don't work that way! 12 \frac{1}{2} means 1 out of 2 equal parts, while 28 \frac{2}{8} means 2 out of 8 equal parts. You need the same sized parts before adding.

How do I know which common denominator to use?

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Look for the smallest number that both denominators divide into evenly. Since 8 ÷ 2 = 4, we can use 8 as our common denominator. This makes the math easier!

Do I always multiply by the same number for both parts?

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No! You only change fractions that don't already have the common denominator. Here, 28 \frac{2}{8} already has denominator 8, so we leave it alone.

What if my answer can be simplified?

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Great question! 68 \frac{6}{8} can be simplified to 34 \frac{3}{4} by dividing both parts by 2. Both answers are correct, but simplified form is usually preferred.

Is there a faster way than finding common denominators?

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For adding fractions, finding a common denominator is the standard method and usually the fastest. Other shortcuts might work sometimes, but this method works every time!

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